An aqueous droplet made in a solution of lipids in oil acquires a lipid monolayer coat, and two such droplets brought into contact form a lipid bilayer at their interface, called a droplet interface bilayer (DIB) (Funakoshi, K. et al. Anal. Chem. 78, 8169-8174 (2006); Holden, M. A. et al. J. Am. Chem. Soc. 129, 8650-8655 (2007)). Similarly, a flat hydrogel support may be used in place of one of the droplets to form a droplet-on-hydrogel bilayer (DHB) (Heron, A. J. et al. J. Am. Chem. Soc. 129, 16042-16047 (2007)). DIBs and DHBs have proved remarkably stable platforms for electrical or optical measurements on single membrane proteins (Holden, M. A. et al., J. Am. Chem. Soc. 129, 8650-8655 (2007); Heron, A. J. et al. J. Am. Chem. Soc. 129, 16042-16047 (2007); Syeda, R. et al., J. Am. Chem. Soc. 130, 15543-15548 (2008); Heron, A. J. et al. J. Am. Chem. Soc. 131, 1652-1653 (2009)). Besides the utility of individual interface bilayers in biophysical measurements, functional networks of droplets joined by DIBs can be constructed that exploit a variety of membrane pumps, channels and pores to act as light sensors, batteries, and electrical devices (Holden, M. A. et al., J. Am. Chem. Soc. 129, 8650-8655 (2007); Maglia, G. et al. Nat. Nanotechnol. 4, 437-440 (2009)). While droplet networks provide a means to build functional devices, they have suffered from an important constraint: the droplets must be surrounded by a bulk oil phase, precluding their use in physiological and other aqueous environments.